I’d like to use this (or something like it) to further my understanding of mathematics, whether that ends at self-directed exploration or more formally at an institution.
Additional Sources:
- soft question - A Learning Roadmap request: From high-school to mid-undergraduate studies - MathOverflow
- Learning the foundations of math - LessWrong
Current Status:
So far I’ve purchased Keith Devlin, Introduction to Mathematical Thinking, which I don’t see in this roadmap but I did see referenced elsewhere (I think in the same reddit thread where I found this roadmap, maybe) as a recommendation for a solid very first step.
Thoughts
It is both extremely discouraging and a little bit tantalizing to see how far down the map statistics first appears. I’ve had this idea in my head that I want to learn statistics, game theory and related for the purpose (i guess?) of getting involved in AI and machine learning.
from this github project on learning mathematics:
The main goal of learning is to understand the ideas and concepts at hand as “deeply” as possible. Understanding is a mental process we go through to see how a new idea is related to previous ideas and knowledge. By “deeply” we mean to grasp as much of the ideas and relations between them as possible.
A good metaphor for this is picturing knowledge as a web of ideas where everything is somehow related to everything else, and the more dense the web is, the stronger it becomes. This means that there might be no “perfect” state of understanding, and otherwise it is an on-going process. You could learn a subject and think you understand it completely, then after learning other subjects, you come back to the first subject to observe that now you understand it deeper.
In this way, the zettlekasten is a projection of the user’s internal progression of understanding on a set of topics. It’s one’s understanding illustrated. But more than that, by working with the web of ideas in order to grow and maintain the zettlekaten a “physical” process is created to enhance as well as confirm the intellectual process of learning.
The learning and reading tips in this document are essentially the Cliff’s Notes for ref_scott-h-young-ultralearning-book